In a scrappy opening period Bradley Wright-Phillips tested Owls goalkeeper Nicky Weaver from a tight angle before Chris Lines' shot at the other end was blocked on the line.
Addicks skipper Jackson then put the visitors ahead in the 28th minute, curling a trademark set-piece into the top right-hand corner from the edge of the area following a foul by Reda Johnson on Bradley Pritchard.
The home side responded to the setback and Lines stung the palms of visiting keeper Ben Hamer with a shot from long distance while left-back Johnson could have levelled when he was allowed a free header inside the box.
Gary Madine did have the ball in the Charlton net in first-half stoppage time but his neat turn and finish was flagged offside.
Wright-Phillips should have extended the away side's lead four minutes after the restart but, after outpacing Wednesday skipper Rob Jones, he was brilliantly denied by Weaver. Clinton Morrison's header was cleared off the line at the death but the league leaders held on.